Laplacian? February 18, 2009

In “The Raincoat,” Matthew Belmonte reflects on his childhood raincoat, an object that represents the tension between himself and his environment, including other people.He compares this tension to the abnormal obsession with controlling the world that is associated with autism.I was particularly struck by his use of the word “Laplacian” to describe himself.I have searched in vain for a definition of Laplacian other than the mathematical term.Why would someone call themselves a “budding Laplacian”?

Although the actual definition of the Laplacian is based in differential calculus, one way that it can be described is in terms of its usefulness.In particular, the Laplacian is used to find equilibrium points in a system.Equilibrium points are points at which there is no movement.These points reflect the feeling Belmonte describes when wearing his raincoat, as though “immersed in the outside worlds flood yet insulated from it.”The areas around these equilibrium points may be moving in several different directions.They may be approaching the equilibrium point or even flying away from it.But the equilibrium point itself is not affected.

In addition, Belmonte discusses how his compulsion to understand the world, and thus reduce it order, pushed him to study science and creative writing, and in particular to describe the world in a mathematically tractable way.As I continue to study applied mathematics, I become more aware of the simplifications that must be made in order to study the world in this way.In the same way that a mathematician studies equilibrium points, Belmonte is looking for stationary rules that describe the best human knowledge of a system.Yet we must always leave things out of our equations for the sake of tractability.Otherwise we would not be able to find solutions.Because of this, equations that try to describe humanity prove to be difficult to create or to analyze.Belmonte tries to find and to convey the equilibrium points of human interaction through science and art.It is due to his participation in this struggle that he can be described as a Laplacian.

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Good guess, and certainly in the same spirit as I was thinking. What was really occupying my thoughts as I wrote that sentence, though, was Laplace’s philosophical work rather than his mathematics — specifically, page 3 of his « Essai philosophique sur les probabilités »: